integrator output Vout.
In mode 3, we measure the motor voltage as a
function of motor current when the motor is running at
constant speed. Since there is no other load, all the motor
current is used to overcome friction.
In Figure 7, we can see that the current required to
overcome friction varies only from about 9 to 11 mA over
the range from 0 to 7V So, in a spin-up from 0 to 7V, we
can compensate for friction by subtracting 10.0 mA from
the measured motor current.
In mode 4, we set the integration stop point to
occur when the rotation rate ƒ is at a precise value. With
7V applied to the motor, adjust VR11 slowly CW until
comparator U3 trips off. This
sets the spin-up stop point at a
known frequency ƒs, measured as
described previously.
Mode 5 is the main
measurement mode — what we’ve
been getting ready for. Press the
reset button to zero the integrator
and the start button to start the
spin-up and the VT integration. When the rotation rate ƒ
reaches the set point ƒs, latch U3 will turn the motor and
the integration off. The DVM will read the 0.1VT product —
the last data point needed to calculate M.
Table 1 is a spreadsheet showing experimental
data and the resulting mass calculation for a range of
drive currents I and cut-off frequencies ƒs — all of which
should produce the same result. The scatter of the results
in Table 1 is a measure of the uncertainty of the mass
determination.
The average of the five measurements shown is 0.213
Kg. I would expect it to be slightly high because I havn’t
accounted for the mass of the rotating parts in the motor
which add about 1% to the total moment of inertia. My
kitchen scale gives the mass of the rotating cylinder as
0.210 Kg.
This little science project tries to give an inkling of
the complexity of metrology research. It
touches a multitude of areas in physics,
electrical engineering, and metrology
including energy, power, and moment
of inertia calculations, op-amp circuit
design, DC motors, error correction,
and uncertainty analysis — a perfect
combination for a physics or EE lab
experiment.
The idea of a fundamental
measurement of mass using a motor and
a spinning flywheel was chosen because
it’s doable with modest hardware and
effort. I’m sure that NV readers will
see a multitude of refinements and
improvements — that is the stuff of
metrology.
Refinement of the much more
complex watt balance is a process that
continues in multiple national standard
laboratories around the world and is
homing in on a mass uncertainty of
three parts in 100,000,000 — roughly
the weight of a fly’s wing relative to the
kilogram. When that happens, the metric
system will finally be defined in terms
of the speed of light, the charge on an
electron, the Planck constant, and the
Cesium frequency. NV
Table 1. Experimental Results.
Mass Experiment Parts List
4 TL071IP U3,U4,U5 Operational Amplifier
1 AD620ANZ U2 Instrumentation Amplifier
1 LM7171BIN U1 Op-Amp 100 mA
2 AGN20012 K12,K40 12V DPDT Relay
1 LT1460GCZ-10#PBF U6 10.00V Reference
1 LS7210 U7 comes with PCB Programmable Timer
3 LEDs 11, 12, 40 Red LED
1 H21A1 OC1 Slotted Optical Switch
2 2N3904 Q15, Q40 NPN Transistor
4 EVQ-11A04M B1,B2,B3,B4 Tactile Switch
3 1N914 D12,D30,D40 Diode
1 MFR-25FBF52-49.9 R3 Resistor 49. 9 ohms 1%
2 MFR-25FBF52-1k R12,R64 Resistor 1K
1 MFR-25FBF52-4.7k R61 Resistor 4.7K
4MFR-25FBF52-15k R1,R11,R13,R14 Resistor15K
3 MFR-25FBF52-10k R2,R41,R42 Resistor 10K 1%
5 MFR-25FBF52-47k R15,R40,R50,R51,R62 Resistor 47K 1%
2 MFR-25FBF52-100k R30,R31 Resistor 100K 1%
1 Digi 496-2316ND C40 Capacitor 0.01 µF
11 Digi 478-3192ND Bypass at op-amps Capacitor 0.1 µF
3 Digi 399-4390ND C1,C12,C64 Capacitor 1 µF
3 Digi 493-1548ND C31,C40,C50 Capacitor 100 µF
1 Jameco 2217781 M1 DC Motor
1 McMaster Carr 7786T12 Flywheel Flywheel, Steel
1 PCB A limited supply is available in the NV webstore and comes with the LS7210* (U7). Gerber files are also available in the downloads.
Cylinder Diameter(D) m 0.0351 0.0351 0.0351 0.0351 0.0351 0.0351
AppliedCurrent A 0.0209 0.026 0.0317 0.0317 0.0317 0.0399
FrictionCurrent A 0.01 0.01 0.01 0.01 0.01 0.01
Effective Current (I) A 0.0109 0.016 0.0217 0.0217 0.0217 0.0299
MeasuredVT V-s 35. 9 21 14. 6 25. 8 30. 2 19
Max RPS (F) Hz 23.81 23. 2 21. 7 29. 4 32. 26 30. 3
CalcMass Kg 0.227 0.205 0.221 0.213 0.207 0.204
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